Carpet

Bajtazar is looking at a carpet in a shop. Some parts of the carpet have ugly manufacturing flaws. He wants to buy as much carpet as he can, so he decided that a piece with one flaw is acceptable. He will stand a large flower pot on that square, so it will not be a problem.

The carpet on sale is a rectangle of height $w$ and width $s$, divided into $w \times s$ squares of size $1 \times 1$. For every square you know whether it is flawed. Bajtazar wants to buy the largest rectangular piece made of these unit squares in which at most one square is flawed. What is the area of that piece?

The first line contains two integers $w$ and $s$ ($1 \le w, s \le 2000$), the height and the width of the carpet. Each of the next $w$ lines describes one row of the carpet, from top to bottom. Each of those lines is a string of $s$ characters, where . is a square without a flaw and # is a flawed square.

Print the largest area of a rectangular piece of carpet that consists of unit squares and contains at most one flawed square.